Method and apparatus for controlling coefficients of adaptive filter

ABSTRACT

A method or apparatus for controlling coefficients of an adaptive filter (3) for identifying unknown system or predicting periodic signals by correcting coefficients of the adaptive filter (3) in such a manner that the difference signal obtained by subtracting an output signal of the adaptive filter (3) from a mixed signal of the output signal from the unknown system and an interference signal comprises steps or means (9) for obtaining the information relating to the magnitude of the coefficients or output of the adaptive filter, and adaptively varying the amount of correction in coefficients of the adaptive filter in response to the obtained information.

This is a continuation of application Ser. No. 07/839,303 filed on Feb.20, 1992, now abandoned.

BACKGROUND OF THE INVENTION

The present invention relates to a method and apparatus for controllingcoefficients of an adaptive filter for identifying an unknown system orpredicting periodic signals using such adaptive filter, whereininterference signals are superimposed with the output signal from theunknown system. Practical applications of this method and apparatusinclude noise cancellers to eliminate noise mixed with a signal from amain input terminal, echo cancellers to eliminate undesired reflectionsignals acoustically coupled to a microphone from a speaker ormismatching of 2-line to 4-line conversion circuit, line equalizers toequalize distortion caused by transmission lines and adaptive lineenhancers to pick up periodic signals buried in a wideband signal or tosuppress periodic interference signals in a wideband signal.

In identifying unknown systems or predicting periodic signals using anadaptive filter, noise cancellers and adaptive line enhancers (referredto as ALE hereunder) are known as typical examples where stronginterference signals are superimposed with an output signal from anunknown system. See p.p. 1692-1716 of the PROCEEDINGS OF IEEE, 1975;Vol. 63, No. 12 (referred to as the Reference 1 hereunder). Also knownare echo cancellers as disclosed in the IEEE JOURNAL ON SELECTED AREASIN COMMUNICATIONS, 1984, Vol. 2, No. 2 at p.p. 283-297 (referred to asthe Reference 2 hereunder). In echo cancellers, if double talk is notdetected properly, the near-end signal acts as a strong interferencesignal. No double talk detection is made in echo cancellers to be usedin 2-line bidirectional transmission. In this case, additional noisesuperimposed in the transmission lines will be a weak interferencesignal to the adaptive operation of the filter.

A noise canceller suppresses noise in the signal by applying a noisereplica corresponding to the noise components in the main inputterminal. Used for this end is an adaptive filter having a transferfunction similar to the impulse response of the noise path from thenoise source to the main input terminal. At this time, a coefficient foreach tap of the adaptive filter is successively modified by correlatingthe reference noise derived at the reference input terminal with adifference signal obtained by subtracting the noise replica from themixed signal of the noise and the signal.

On the other hand, an echo canceller suppresses the echo by subtractinga pseudo echo or an echo replica from the echo signal caused bymismatching of the 2-line to 4-line conversion circuit in a 2-linebidirectional transmission line or a long distance telephone line oracoustical coupling between a microphone and a speaker. The echo replicais generated by using an active filter having a transfer functionsimilar to the impulse response of the echo path. A coefficient of eachtap at the adaptive filter is successively modified by correlating thereference signal at the reference input terminal with a differencesignal obtained by subtracting the echo replica from the mixed signal ofthe echo signal and the additional noise.

Used in ALEs is an adaptive filter having a transfer function to passonly signal components whose periods are equal to those of the periodicsignals for enhancing the periodic signals buried in a wideband signal.A coefficient of each tap of the adaptive filter for this application isa prediction coefficient to predict the periodic signals. It issuccessively modified by correlating the difference signal obtained bysubtracting the predicted periodic signals or the output from theadaptive filter from the mixed signal of the periodic signals and thewideband signal on the main input terminal with the delayed mixed signalon the reference input. For enhancing the periodic signals, the outputfrom the adaptive filter is used as the ALE output and the ALE is alsoused to suppress periodic interference signal to the wideband signal. Inthe latter case, the output signal is the difference or error signalinstead of the output from the adaptive filter.

There are two typical coefficient modifications or convergingalgorithms. One is an LMS algorithm (see the Reference 1). The other isa Learning Identification Method (LIM) as set forth in p.p. 282-287 ofThe IEEE Transactions on Automatic Control, Vol. 12, No. 3 in 1967(referred to as Reference 3 hereunder).

Illustrated In FIG. 14 is a block diagram of a conventional noisecanceller. A mixed signal of a signal and noise detected on a main inputterminal 1 is supplied to a subtracter 4. On the other hand, supplied toan adaptive filter 3 is a reference noise detected on a reference inputterminal 2. The noise components are cancelled by the subtracter 4 whichsubtracts the noise replica generated by the adaptive filter 3 from themixed signal. The subtracted output is supplied to an output terminal 6.Simultaneously, the output of the subtracter 4 is supplied to amultiplier 5 to be multiplied by the coefficient 2α to be used forcorrecting the coefficient of the adaptive filter 3. Here, α is aconstant and 2α is known as a step size. Let the signal, the referencenoise, the noise to be cancelled and an additional noise to the signalbe S_(k) (k being an index to represent time), n_(k), V_(k) and δ_(k),respectively. The signal u_(k) to be actually supplied to the subtracter4 from the input terminal 1 is given by the following expression:

    u.sub.k =S.sub.k +V.sub.k +δ.sub.k                   ( 1)

A purpose of the noise cancellers is to generate the noise replica V_(k)of the noise components v_(k) in the above expression (1) for cancellingthe noise. The noise replica V_(k) is adaptively generated by using aclosed loop comprising the adaptive filter 3, the subtracter 4 and themultiplier 5 in FIG. 14. The closed loop provides the difference orerror signal d_(k) given by the following expression as the outputsignal from the subtracter 4. However, it is to be noted that δ_(k) issufficiently small as compared to S_(k) and is neglected in theexpression:

    d.sub.k =S.sub.k +v.sub.k -V.sub.k                         ( 2)

In the above expression (2), (v_(k) -V_(k)) is known as a residualnoise. In the LMS algorithm, the m-th coefficient C_(m),k of theadaptive filter 3 is corrected in accordance with the followingexpression:

    C.sub.m,k +C.sub.m,k-1 +2α·d.sub.k ·n.sub.m,k-1 ( 3)

A matrix format of the expression (3) for all of the N coefficients isas follows:

    C.sub.k =C.sub.k-1 +2α·d.sub.k ·n.sub.k-1 ( 4)

Where, C_(k) and n_(k) are given by the following expressions,respectively:

    C.sub.k = C.sub.0 C.sub.1 . . . C.sub.N-1 !.sup.T          ( 5)

    n.sub.k = n.sub.k n.sub.k-1 . . . n.sub.K-N+1 !.sup.T      ( 6)

Here, .!^(T) represents a transposition of the matrix. On the otherhand, in the LIM algorithm, correction of coefficients will be carriedout in accordance with the following expression (7) rather than theexpression (4).

    C.sub.k =C.sub.k-1 +(2μ/Nσn.sup.2)·d.sub.k ·n.sub.k-1                                       ( 7)

μ in the above expression (7) is the step size for LIM and σ_(n) ²represents an average power of the input to the adaptive filter 3. σ_(n)² is used to make the step size μ counter proportional to the averagepower for stable convergence. There are a few methods to calculate σ_(n)². One example is to calculate in accordance with the followingexpression (8): ##EQU1##

The step sizes in the above expressions (4) and (7) define theconverging speed of the adaptive filter and the residual noise levelafter convergence. In case of the LMS algorithm, if the value of α islarger, the convergence speed is faster but the final residual noiselevel increases. On the contrary, it is required to choose relativelysmall value of α in order to achieve a sufficiently low final residualnoise level. However, this causes a relatively slow convergence speed.This is true of the step size μ in the LIM algorithm.

A VS algorithm has been proposed in order to meet the conflictingrequirements in the step size to the converging speed and the finalresidual noise. See p.p. 309-316 of the IEEE Transactions on Acoustics,Speech and Signal Processing, 1986, Vol. 34, No. 2 (referred to asReference 4 hereunder). The VS algorithm uses step size matrix 2Ainstead of the step size 2α in the LMS algorithm as represented by theabove expression (4). Each component of A is controlled in response tothe progress in convergence of the adaptive filter. The use ofindividual step size given by the step size matrix A rather than acommon step size for each coefficient allows optimum step size for eachcoefficient depending on variations in magnitude of the self-correlationmatrix component, thereby improving the converging speed. Actualcorrection of the coefficients will be performed by the followingexpression: ##EQU2## a_(m),m is determined by the successive pattern ofthe polarity sgn G_(m),k ! of the gradient component G_(m),kcorresponding to the m-th tap, where G_(m),k is given by the followingexpression:

    G.sub.m,k =2·α.sub.m,m ·d.sub.k ·n.sub.m,k-1                                     ( 10)

In an ideal case where d_(k) =v_(k) -V_(k), the polarity of G_(m),kdirectly represents the progress of convergence. However, d_(k) isgenerally affected by S_(k) as understood from the expression d_(k)=S_(k) +v_(k) -V_(k). In order to reduce the influence of S_(k), a_(m),mis halved if sgn G_(m),k ! changes m₀ times consecutively. On the otherhand, it is doubled if sgn G_(m),k ! are equal for m₁ timesconsecutively. That is, the VS algorithm features to make equivalentlyS_(k) +v_(k) -V_(k) ∝v_(k) -V_(k) by detecting succession of identicalpolarities or successive alternations of the polarity. However, there isa certain limitation In the variable range of a_(m),m. That is, themaximum value α_(max) =1/λ and the minimum value α_(min) is defined by adesired final residual noise. Here, λ is the maximum inherent value ofthe autocorrelation matrix. The performance of the VS algorithm dependslargely on the relationship between S_(k) and v_(k) -V_(k). The polaritychanging pattern of the above G_(m),k is a function of thesignal-to-noise ratio (SNR) and the spectrum of S_(k). When the SNR islarge, |S_(k) |>|v_(k) -V_(k) | is almost always true and seriouslyaffects polarity detection. Considering the fact that SNR is defined bythe ratio of the signal and the noise in mathematical expectation oftheir instantaneous powers, |S_(k) |>|v_(k) -V_(k) | is satisfied with agreater probability as S_(k) contains more higher-frequency componentseven if SNR is low. In other words, when S_(k) has many peaks and dips,it is most likely that |S_(k) | is larger than |v_(k) -V_(k) | in someof the peaks even if SNR is sufficiently low.

Illustrated in FIG. 15 is a block diagram of a conventional ALEcorresponding to the noise canceller in FIG. 14. A mixed signal to besupplied to an input terminal 1 comprises a wideband signal S_(k), aperiodic signal v_(k) and an additive noise δ_(k). On the other hand,supplied to an adaptive filter 3 is a delayed signal of the mixed signalon the input terminal 1 delayed by L by a delay element 8 and is givenby:

    u.sub.k-L =S.sub.k-L +V.sub.K-L                            ( 11)

However, δ_(k) is neglected in the above expression (11) because it issufficiently small compared with S_(k). The difference signal d_(k)given by the expression (2) is obtained by subtracting the predictionsignal V_(k) of v_(k) generated by the adaptive filter 3 from the mixedsignal u_(k) of the expression (1). Derived from an output terminal 6 isa wideband signal with suppressed periodic interference signals. Alsoderived from an output terminal 7 is the enhanced periodic signalsobtained by suppressing wideband noise. Coefficient correction of theadaptive filter 3 should be carried out by using (v_(k) -V_(k)) which isa prediction error of the periodic signals. However, the actuallyderived difference signal d_(k) contains the wideband signal S_(k). As aresult, the above discussions on |S_(k) | and |v_(k) -V_(k) | in thenoise canceller are also applicable to the ALE. That is, a correct stepsize control in the VS algorithm depends on the relationship between|S_(k) | and |v_(k) -V_(k) | and no correct step size is obtained if|S_(k) | is larger than |v_(k) -V_(k) |.

Illustrated in FIG. 16 is a block diagram of a conventional echocanceller corresponding to the noise canceller in FIG. 14. The blockdiagrams in FIGS. 16 and 14 are identical to each other but differ onlyin input signals. Supplied to an input terminal 1 is a signal comprisingan echo V_(k) and an additive noise δ_(k).

    u.sub.k =v.sub.k +δ.sub.k                            ( 12)

On the other hand, supplied to an adaptive filter 3 is n_(k) through aninput terminal 2. n_(k) represents an input signal to a 2-line to 4-lineconversion transformer in case of a bidirectional transmission circuitor a signal to be supplied to a speaker in case of an echo due toacoustic coupling. An echo replica V_(k) of v_(k) generated by theadaptive filter 3 is subtracted from u_(k) in the expression (12)derived from the input terminal 1 to obtain the difference signal d_(k)in the following expression (13):

    d.sub.k =v.sub.k -V.sub.k +δ.sub.k                   ( 13)

Derived from an output terminal 6 is the echo cancelled signal.Coefficient correction of the adaptive filter 3 should be performedusing the residual echo (v_(k) -V_(k)). In practice, however, theadditional noise δ_(k) is contained in the difference signal d_(k).Although δ_(k) is fairly small in general, it interferes the residualecho when the residual echo becomes sufficiently small.

SUMMARY OF THE INVENTION

In order to minimize the effect of interference signals, it is requiredto increase both m₀ and m₁ and minimize α_(min). However, this willadversely make the advantage of the VS algorithm less attractive.Additionally, as understood from the expression (9), the VS algorithmrequires that a large number of step sizes equal to the number ofcoefficients be stored in a memory, thereby requiring a large memorycapacity as the number of taps increases and in turn making the hardwarevery expensive.

It is therefore an object of the present invention to provide a methodand an apparatus for controlling coefficients of an adaptive filter witha shorter converging time and smaller scale of hardware.

According to the present invention there is provided a method orapparatus for controlling coefficients of an adaptive filter foridentifying an unknown system and predicting periodic signals bycorrecting coefficients of the adaptive filter in such a manner that thedifference signal is obtained by subtracting an output signal of theadaptive filter from a mixed signal consisting of the output signal fromthe unknown system and an interference signal. The present inventionincludes an apparatus and method for obtaining the information relatingto the magnitude of the coefficients or output of the adaptive filter,and adaptively varying the amount of correction in coefficients of theadaptive filter according to the obtained information.

The coefficient control method and apparatus for an adaptive filteraccording to the present invention reduces converging time bycontrolling the magnitude of the step size by using the fact that theabsolute values of coefficients of the adaptive filter increase andsaturate as the coefficients converge. Since the absolute values ofcoefficients depend on the transfer function of the path to beidentified, such dependency can be avoided by using the ratio of thelong-time and short-time averages in the average value of thecoefficients. Since the absolute value of the coefficients as well asthe average value of the absolute signal output from the adaptive filtersaturate to a constant value, the converging time can be reduced bycontrolling the step size using the information relating to themagnitude of the filter output signal instead of the informationrelating to the magnitude of the filter coefficients.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of one embodiment of the present invention;

FIG. 2 is a detailed schematic of the adaptive filter 3 in FIG. 1;

FIG. 3 is a first example of an information extraction circuit 9;

FIG. 4 is a second example of an information extraction circuit 9;

FIG. 5 is one example of an arithmetic circuit 10 to obtain y_(k) ;

FIG. 6 is an example of the averaging circuit;

FIG. 7 is an example of the divider circuit 54;

FIG. 8 is an example of the inverse circuit 32;

FIG. 9 is a block diagram of adaptively controlling the step size usingthe filter output;

FIG. 10 is a block diagram of ALE according to the present inventioncorresponding to the noise canceller in FIG. 1;

FIG. 11 is a block diagram of ALE according to the present inventioncorresponding to the noise canceller in FIG.2;

FIGS. 12 and 13 are block diagrams of applying the present invention toan echo canceller;

FIG. 14 is a block diagram of a conventional noise canceller;

FIG. 15 is a block diagram of a conventional ALE corresponding to thenoise canceller in FIG. 14; and

FIG. 16 is a block diagram of a conventional echo cancellercorresponding to the noise canceller in FIG. 14.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described in detail hereunder by referenceto the accompanying drawings. Illustrated in FIG. 1 is a block diagramof one embodiment of the present invention. In FIG. 1, the samereference numerals as those in FIG. 14 are used to refer like functionalblocks. A primary difference between FIGS. 1 and 14 is in the magnitudeof the step size. That is, the step size 2α to be supplied to themultiplier 5 in FIG. 14 is fixed but varies in FIG. 1 in response to themagnitude of coefficients for the adaptive filter. For this end, thereis employed an information extraction circuit 9 to extract theinformation relating to the magnitude of coefficients. Also employed inFIG. 1 is an arithmetic circuit 10 for controlling the step size usingthe extracted information.

By reference to FIG. 1, supplied to the information extraction circuit 9are the adaptive filter coefficients from the adaptive filter 3. Theinformation extraction circuit 9 extracts the information relating tothe magnitude of coefficients for supplying to the arithmetic circuit10. The arithmetic circuit 10 performs arithmetic operation as definedby b=f a! based on the signal a to be supplied from the informationextraction circuit 9 and the output is supplied to the adaptive filter3.

Illustrated in FIG. 2 is a detailed block diagram of the adaptive filter3 in FIG. 1. For convenience, it is assumed that the adaptive filter 3has only 2 taps. An input signal from the input terminal 2 in FIG. 1 issupplied to an input terminal 201 in FIG. 2. Also, supplied to an inputterminal 209 is the output from the subtracter 4 in FIG. 1, or the errorsignal. The output signal on an output terminal 212 is supplied to thesubtracter 4 as the output of the adaptive filter 3 in FIG. 1. Bothsignals from output terminals 222 and 223 are supplied to theinformation extraction circuit 9. The output signal of the arithmeticcircuit is supplied to an input terminal 221.

The input signal to be supplied to the input terminal 201 is supplied toa delay element 202 and multipliers 205 and 207. The input signal on theinput terminal 201 is also supplied to multipliers 206 and 208 after adelay equivalent to one sampling period. In other words, the signals tobe supplied to the multipliers 205-206 and 207-208 have a timedifference equal to one sampling period. Now, the input signal sample tobe supplied to the input terminal 201 at time kT (T representing thesampling period) is represented as n_(k). n_(k) and n_(k-1) are suppliedto the multipliers 205-207 and 206-208, respectively. On the other hand,let d_(k) and y_(k) be the error signal supplied to a multiplier 210from the input terminal 209 and the signal supplied to the multiplier210 from the arithmetic circuit 10 by way of the input terminal 221,respectively. Then, the output from the multiplier 210 is equal to2α·y_(k) ·d_(k). The output of the multiplier 210 is multiplied by theinput signals n_(k) and n_(k-1) in the multipliers 205 and 206 beforebeing transferred to adders 213 and 214, respectively. That is, thesignals to be supplied to the adders 213 and 214 are 2α·y_(k) ·d_(k)·n_(k) and 2α·y_(k) ·d_(k) ·n_(k-1), respectively. Fedback respectivelyto the adders 213 and 214 are the outputs from delay elements 203 and204, respectively. The outputs from the delay elements 203 and 204 arecoefficients for the adaptive filter 3 and are represented by C₀,k andC₁,k at respective time kT. Then, the added outputs transmitted to thedelay elements 203 and 204 from the adders 213 and 214 will be C₀,k+2α·y_(k) ·d_(k) ·n_(k) and C₁,k +2α·y_(k) ·d_(k) ·n_(k-1),respectively. These signals are delayed by one sampling period becauseof the delay elements 203 and 204. Therefore,

    C.sub.0,k+1 =C.sub.0,k +2α·y.sub.k ·d.sub.k ·n.sub.k                                         (14)

    C.sub.1,k+1 =C.sub.1,k +2α·y.sub.k ·d.sub.k ·n.sub.k-1                                       (15)

C₀,k and C₁,k are supplied to the output terminals 214 and 215respectively for step size control.

Illustrated in FIG. 3 is a block diagram of a first example of theinformation extraction circuit 9, wherein a squared value of thecoefficient is used as the information relating to the magnitude of thecoefficients of the adaptive filter. Supplied to input terminals 30₀,30₁, . . . , 30_(N-1) are N coefficients from the adaptive filter 3. Itis to be noted here that N is the number of taps of the adaptive filter3. N=2 is the particular example of the adaptive filter 3 in FIG. 2. Thesignals supplied to the input terminals 30₀, 30₁, . . , 30_(N-1) aresquared by respective squaring circuits 31₀, 31₁, . . . , 31_(N-1) to besupplied to a multi-input adder 32. The multi-input adder 32 providesthe sum of the squared values to be derived from its output terminal 33.Referring to the description for FIG. 2, the signal a_(k) derived fromthe output terminal 33 is given by the following expression: ##EQU3##

Illustrated in FIG. 4 is a block diagram of a second example of theinformation extraction circuit 9, wherein absolute values of thecoefficients are used as the information relating to the magnitude ofthe coefficients of the adaptive filter. It is to be noted that theabsolute value of each coefficient saturates as adaption of the adaptivefilter coefficients progresses, thereby saturating the sum of theabsolute values. Accordingly, the absolute values can be used as ameasure to determine the degree of convergence. That is, the step sizecan be controlled by the sum of the absolute values of the filtercoefficients instead of the squared values thereof. Supplied to theinput terminals 30₀, 30₁, 30₂, . . . , 30_(N-1) are N coefficients fromthe adaptive filter 3, which are then converted into the correspondingabsolute values by absolute value circuits 41₀, 41₁, . . . , 41_(N-1)before being supplied to the multi-input adder 32. The multi-input adder32 operates to provide from its output terminal 33 the sum of theabsolute values a_(k) which is given by the following expression:##EQU4##

For simplicity, a description is given hereunder for a case where a_(k)is defined by the expression (16).

The obtained a_(k) is supplied to the arithmetic circuit 10 whichcalculates and provides an output b_(k) in accordance with thedefinition b_(k) =f a_(k) !. The calculated output b_(k) is fed to theadaptive filter 3 by way of the input terminal 213. Therefore, ##EQU5##

The equations (14), (15) are basically the same as the equation (3).Only the difference is the use of a variable step size 2α·y_(k) insteadof the fixed step size 2α. A method of controlling y_(k), i.e., how tocalculate f .! is an essential factor to achieve high-speed, stableconvergence.

Illustrated in FIG. 5 is a block diagram of the arithmetic circuit 10 toobtain y_(k). The input signal derived from the input terminal 51 is fedto both averaging circuits 52, 53. That is, the inputs to the averagingcircuits 52, 53 are a_(k) or the output from the information extractioncircuit 9. The averaging circuit 52 calculates a short-time-constantmoving average a_(k) of the input signal while the averaging circuit 53calculates a long-time-constant moving average a_(k) ! of the inputsignal. The outputs u_(k) and z_(k) from the averaging circuits 52 and53 are given by the following expressions, respectively: ##EQU6##

The divider 54 calculates the ratio of u_(k) and z_(k) to provide on itsoutput terminal 55 y_(k) given by the following expression: ##EQU7##

Now, a_(k) increases and saturates as k increases. The short-timeaverage a_(k) increases faster than the long-time average a_(k) !. As aresult, it is understood that the ratio y_(k) =a_(k) / a_(k) ! decreasesgradually from a value larger than 1 to converge ultimately to 1. Thismeans that the signal y_(k) to be supplied to the output terminal 55from the divider 54 is relatively large Immediately after initiation ofthe coefficient correction but decreases gradually as the adaptivefilter 3 continues its adaptation. Finally, it becomes equal to 1. Thesignal y_(k) as obtained in the above manner is fed to the inputterminal 213 in FIG. 2 as the output from the arithmetic circuit 10 inFIG. 1.

The use of this value y_(k) multiplied by the fixed step-size inaccordance with the equations (14) and (15) will make the effectivestep-size large initially and subsequently equal to the final value 2αafter convergence, thereby shortening the converging time.

Illustrated in FIG. 6 is a block diagram of the averaging circuit whichis known as a first-order leaky integrator with a leaky factor β(0<β<1).A signal supplied to its input terminal 61 is multiplied by the factorof β in an integrator 62 before being fed to an adder 63. The outputfrom the adder 63 is fed to an output terminal 66 and also to a delayelement 65. A delayed signal delayed by one clock period in the delayelement 65 is multiplied by the coefficient of 1-β in a multiplier 64before being fed to the adder 63. The adder 63 accumulates the signalsfed to the input terminal 61 with 1 clock delay, thereby integrating thesignals. At this time, "leak" will be caused in the multiplier 64. Asunderstood from the values of the multipliers 62 and 64, when the signalfed to the input terminal 61 is relatively stationary, the output signalfrom the output terminal 66 increases gradually before saturating. Byproper selection of the constant β, the saturation value can stimulatethe average value of the input signal. If β is small, 1-β isapproximately 1 and the signal on the output terminal 66 is fed back tothe adder 63 with no modification, thereby providing a moving averagingcircuit of relatively long time constant. On the other hand, if β islarge, the feedback signal from the output terminal 66 to the adder 63will be rapidly decreasing. This will increase the contribution of thecurrent signal fed to the multiplier 62 from the input terminal 61,thereby shortening the time constant of the moving averaging circuit.Accordingly, it is understood that the averaging circuit as illustratedin FIG. 6 can be used for the averaging circuits 52 and 53 by properselection of the leaky factor β. When the first-order leaky integratorin FIG. 6 is used for the averaging circuits 52 and 53, the leakyfactors of the averaging circuits 52 and 53 are chosen respectively asβ_(s) and β₁ to obtain the following equations from the above equations(19) and (20): ##EQU8##

As a result, y_(k) is expressed as follows: ##EQU9##

Considering that y_(k) is a decreasing function with z₀ =u₀ =0, themaximum value of y_(k) is y₁ =β_(s) /β₁ and is constant regardless ofany external condition such as coefficients of the adaptive filter andthe reference signals therefor. Although FIG. 6 illustrates an exampleof a recursive type averaging circuit, any other circuit configurationsuch as a transversal type may be used as well.

Illustrated in FIG. 7 is a block diagram of the divider 54 comprising aninverter and a multiplier. The signals fed to the divider 54 in FIG. 5from the averaging circuits 52 and 53 are fed to input terminals 70 and71, respectively. The inverter 72 provides an inverse of the signal fedto the input terminal 71 to be transferred to the multiplier 73 wherethe inverse signal and the signal from the input terminal 70 aremultiplied before being transferred to an output terminal 74. Theproduct on the output terminal is fed to the output terminal 55 in FIG.5.

Illustrated in FIG. 8 is a block diagram of one example of the inversecircuit 32 to simulate the inverse calculation using exponent. Let asignal to be inverted be p_(k) and the inverse q_(k) =1/p_(k), q_(k) maybe approximated by the following linear equation:

    q.sub.k =-2.sup.-2r-1 p.sub.k +2.sup.-r-1 (2.sup.-1 +1)    (25)

Here, r is the largest integer not exceeding log₂ (p_(k)). The equation(25) is simple to realize because it comprises exponent of 2 andadditions and subtractions. The inverter in FIG. 8 operates as follows:

Applied to an input terminal 800 in FIG. 8 is the signal to be fed tothe inverter 72 from the input terminal 71 in FIG. 7. The signal is fedto an amplitude evaluation circuit 801 and a multiplier 809. Theamplitude evaluation circuit 801 calculates the maximum integer r notexceeding log₂ (p_(k)) for the input signal p_(k). The maximum integer ris fed to a multiplier 802 which is multiplied by -1 before beingtransmitted to adders 803 and 804. In the adder 803, -1 is added to thesignal from the multiplier 802 to obtain -r-1 to be fed to an addressgeneration circuit 806. Added to the signal from the multiplier 802 inthe adder 804 is -r-1, or the output from the multiplier 803 to feed theresulting signal -2r-1 to the address generation circuit 805. Theaddress generation circuits 805 and 806 generate respective addresses toa RAM 807 for obtaining from the RAM exponents of 2 corresponding to thefed signals. The RAM 807 supplies to a multiplier 802 2^(-2r-1)corresponding to the address generation circuit 805 while 2^(-r-1) issupplied to a multiplier 810 in response to the address generationcircuit 806. The multiplier 810 multiplies the signal fed from the RAM807 by 1.5 before being fed to a multiplier 811. The adder 808multiplies the signal fed from the RAM 807 by -1 before being fed to themultiplier 809. The signal -2^(-2r-1) fed to the multiplier 809 ismultiplied by the input signal p_(k) fed from the input terminal 800 tobe fed to the adder 811. The adder 811, then, adds the signal -2^(-2r-1)p_(kk) from the multiplier 809 and the signal 1.5·2^(-r-1) from themultiplier 810 to derive the resulting output -2^(-2r-1) ·p_(k)+1.5·2^(-r-1) from an output terminal 812. The output signal from theoutput terminal 812 is the signal to be fed to the multiplier 73 in FIG.7.

It is assumed so far that a_(k) is defined by the equation (16), i.e.,the sum of the squared values of filter coefficients is fed to thearithmetic circuit 10. However, it is to be understood that thedescriptions also apply to a_(k) defined by the equation (17), i.e., thesum of the absolute values of filter coefficients is fed to thearithmetic circuit 10. Also, similar descriptions hold true for adaptivefilters having more than 2 taps.

Although the above descriptions are made on the step-size control usingthe sum of the squared values of the filter coefficients, it is to beunderstood that the step-size control may be made using the informationrelating to the magnitude of the filter output signal instead of thefilter coefficients because the average values of the adaptive filteroutput in either absolute or squared values will saturate as well as theabsolute values in the coefficients to a stationary or a pseudostationary input signal. Illustrated in FIG. 9 is a block diagram foradaptively controlling the step size using the filter output. Adifference from the embodiment as illustrated in FIG. 1 is in that thesignal to be supplied to the information extraction circuit 9 is theoutput from the adaptive filter 3. As a result, there is only one inputin the information extraction circuit 9. However, the same constructionas illustrated in FIG. 3 or FIG. 4 may be used without any correction.When there are more than one input terminals in the informationextraction circuit 9, either one of the terminals may be used to feedthe output from the adaptive filter 3 thereto. Also, the adaptive filter3 may be the same as illustrated in FIG. 2 with leaving the outputterminals 214 and 215 unconnected.

When the first example in FIG. 3 is used as the information extractioncircuit 9, the signal a_(k) on the output terminal 33 will be expressed:##EQU10##

On the contrary, when the second example in FIG. 4 is used as theinformation extraction circuit 9, the signal a_(k) derived from theoutput terminal 33 will be expressed: ##EQU11##

For simplicity, in a case where a_(k) is defined by the equation (26),the following equations will be obtained in corresponding to theequations (18) through (24): ##EQU12##

Other circuit operations are identical to those as described above byreference to FIG. 1 and no detailed descriptions will be given herein.

Illustrated in FIG. 10 is a block diagram of the ALE according to thepresent invention corresponding to the noise canceller in FIG. 1. Themixed signal supplied to the input terminal 1 comprises a widebandsignal S_(k), a periodic signal v_(k) and an additional noise δ_(k). Fedto the adaptive filter 3 is the mixed signal on the input terminal 1delayed by the time L In the delay element 8, or the signal u_(k-L)given by the equation (11). A predicted signal V_(k) of v_(k) asgenerated by the adaptive filter 3 is subtracted from the mixed signalu_(k) to obtain the difference signal d_(k) as given by the equation(2). Derived from output terminals 6 and 7 are the wideband signal withsuppressed periodic interference signal and the periodic signal enhancedby suppressing the wideband noise. Coefficient correction of theadaptive filter 3 will be carried out in the exactly same manner as theembodiment in FIG. 1 using the filter coefficients.

Illustrated in FIG. 11 is a block diagram of the ALE according to thepresent invention corresponding to the noise canceller in FIG. 9. Therelationship between the embodiments in FIGS. 11 and 10 is equal to thatbetween the embodiments in FIGS. 9 and 1, thereby requiring no detaileddescription of FIG. 11.

The present invention is also applicable to an echo canceller.Illustrated in FIGS. 12 and 13 are embodiments to apply the presentinvention to an echo canceller. FIGS. 12 and 13 are simply replacementof S_(k) +v_(k) and S_(k) +v_(k) -V_(k) by v_(k) +δ_(k) and v_(k) -V_(k)+δ_(k) in FIGS. 1 and 9. Accordingly, no detailed description will begiven herein.

As described hereinbefore, a difference between LIM and LMS is the useof the step size μ divided by the average power σ_(n) ² fed to theadaptive filter 3 instead of α. The method of varying the step size inthe above description in connection with the present invention will beapplied to LIM without any correction.

What is claimed is:
 1. A method of controlling coefficients of anadaptive filter, said method comprising the steps of:obtaining a mixedsignal by combining an interference signal with an output signal from anunknown system; obtaining an output signal generated by said adaptivefilter, and subtracting said output signal generated by said adaptivefilter from said mixed signal to obtain a difference signal; obtaining asquare value of the output signal generated by the adaptive filter, andutilizing said square value of the output signal of the adaptive filteras obtained information relating to magnitude of the coefficients ofsaid adaptive filter; and adaptively varying corrections applied to thecoefficients of said adaptive filter according to said obtainedinformation.
 2. A method as defined in claim 1, alsocomprising:obtaining information relating to a short-time averagemagnitude and a long-time average magnitude of the coefficients of saidadaptive filter and utilizing said information to obtain a ratio betweensaid short-time average magnitude and said long-time average magnitude;wherein said step of adaptively varying corrections applied to thecoefficients of said adaptive filter includes the step of adaptivelyvarying the amount of the corrections applied to the coefficients ofsaid adaptive filter according to the ratio between the short-timeaverage magnitude and the long-time average magnitude of thecoefficients of said adaptive filter.
 3. A method of controllingcoefficients of an adaptive filter, said method comprising the stepsof:obtaining a mixed signal by combining an interference signal with anoutput signal from an unknown system; obtaining an output signalgenerated by said adaptive filter, and subtracting said output signal ofsaid adaptive filter from said mixed signal to obtain a differencesignal; obtaining an absolute value of the output signal generated bythe adaptive filter, and utilizing said absolute value of the outputsignal generated by the adaptive filter as obtained information relatingto magnitude of the coefficients of said adaptive filter; and adaptivelyvarying corrections applied to the coefficients of said adaptive filteraccording to said obtained information.
 4. A method as defined in claim3, also comprising:obtaining information relating to a short-timeaverage magnitude and a long-time average magnitude of the coefficientsof said adaptive filter and utilizing said information to obtain a ratiobetween said short-time average magnitude and said long-time averagemagnitude; wherein said step of adaptively varying corrections appliedto the coefficients of said adaptive filler includes the step ofadaptively varying the amount of the corrections applied to thecoefficients of said adaptive filter according to the ratio between theshort-time average magnitude and the long-time average magnitude of theinformation on the magnitude of the output signal.
 5. A method asdefined in claim 4, wherein said step of utilizing said information toobtain the ratio between the short time average magnitude and long timeaverage magnitude comprises the steps of inverting the long time averagemagnitude to obtain an inverted signal and multiplying the invertedsignal by the short time average magnitude, wherein the step ofinverting is made by a linear approximation of an exponent of
 2. 6. Amethod as defined in claim 5, wherein the step of inverting includes thestep of determining a variable X according to a linear approximation of-2^(-2-r) X+2^(-r-1) (2⁻¹ +1) using the maximum integer r not exceedinglog₂ (x).
 7. Electronic filter apparatus comprising:an adaptive filterwhich upon receiving a reference signal generates a pseudo output for anunknown system; first means for generating a mixed signal frominterference signals and an output signal of the unknown system; a firstsubtracter for subtracting the pseudo output from said mixed signal; aninformation extraction circuit that receives coefficients for theadaptive filter to extract the information on the magnitude of saidcoefficients and generate an output (a); an arithmetic circuit toreceive the output (a) for calculating and providing a signal (b) whichdecreases as the output (a) increases or increases as the output (a)decreases; second means for correcting the coefficients of the adaptivefilter utilizing the outputs from the first subtracter, said arithmeticcircuit and the reference signal; and said information extractioncircuit comprising a square circuit for developing the output of saidadaptive filter.
 8. Electronic filter apparatus as set forth in claim 7,wherein said arithmetic circuit comprises a first average circuit foraveraging an input signal with a first parameter, a second averagecircuit for averaging the input signal with a second parameter thatdiffers from the first parameter in said first average circuit, and adivider for developing a ratio of an output of said first averagecircuit and an output of said second average circuit.
 9. Electronicfilter apparatus as in claim 8 wherein said divider comprises aninverter for outputting an inverted signal of the output from saidsecond average circuit and a first multiplier for multiplying theinverted signal with the output from said first average circuit. 10.Electronic filter apparatus as set forth in claim 7 wherein saidinformation extraction circuit comprises additional square circuitswhich together with said square circuit form a group of square circuitseach developing a squared value of each coefficient value; and a summerfor developing a summed value of outputs of said group of squarecircuits.
 11. Electronic filter apparatus as in claim 7 wherein saidarithmetic circuit is an inverse circuit comprising:an amplitudeevaluation circuit to provide the maximum integer r not exceeding log₂(X) of an input signal X; a second multiplier to multiply the output ofsaid amplitude evaluation circuit by -1; a second adder to add -1 to theout/put of said second multiplier; a third adder to provide the sum ofthe outputs of said second multiplier and said second adder; a firstaddress generation circuit to provide a RAM address signal to give anexponent of 2 corresponding to the output of said third adder; a secondaddress generation circuit to provide a RAM address signal to give anexponent of 2 corresponding to the output of said second adder; a RAM toprovide a corresponding exponent output of 2 on receiving the outputs ofsaid first and second address generation circuits; a third multiplier tomultiply the output corresponding to the address generated from saidfirst address generation circuit in said RAM by -1; a fourth multiplierto multiply the output of said third multiplier by the input signal tothe input terminal; a fifth multiplier to multiply the outputcorresponding to the address generated by said second address generationcircuit in said RAM by 1.5; and a fourth adder to add the outputs ofsaid fifth and fourth multipliers for outputting from the outputterminal.
 12. Electronic filter apparatus comprising:an adaptive filterwhich upon receiving a reference signal generates a pseudo output for anunknown system; first means for generating a mixed signal frominterference signals and an output signal of the unknown system; a firstsubtracter for subtracting the pseudo output from said mixed signal; aninformation extraction circuit comprising a circuit that receivescoefficients for the adaptive filter to extract the information on themagnitude of said coefficients and generate an output (a); an arithmeticcircuit to receive the output (a) for calculating and providing a signal(b) which decreases as the output (a) increases or increases as theoutput (a) decreases; second means for correcting the coefficients ofthe adaptive filter utilizing the outputs from the first subtracter,said arithmetic circuit and the reference signal; and said informationextraction circuit also comprising an absolute value circuit fordeveloping an absolute value of the output of said adaptive filter. 13.Electronic filter apparatus as set forth in claim 12 wherein saidinformation extraction circuit further comprises additional absolutevalue circuits which together with other portions of said informationextraction circuit form a group of absolute value circuits eachdeveloping an absolute value of each coefficient value, and a firstsummer for developing a summed value of the outputs of said group ofabsolute value circuits.
 14. Electronic filter apparatus comprising:anadaptive filter which upon receiving a reference signal generates apseudo output for an unknown system; first means for generating a mixedsignal from interference signals and an output signal of the unknownsystem; a first subtracter for subtracting the pseudo output from saidmixed signal; an information extraction circuit that receives the outputsignal for the adaptive filter to extract the information on themagnitude of coefficients for the adaptive filter and generate an output(a); an arithmetic circuit to receive the output (a) for calculating andproviding a signal (b) which decreases as the output (a) increases orincreases as the output (a) decreases; second means for correcting thecoefficients of the adaptive filter utilizing the outputs from the firstsubtracter, said arithmetic circuit and the reference signal; and saidinformation extraction circuit comprising a square circuit fordeveloping the output of said adaptive filter.
 15. Electronic filterapparatus comprising:an adaptive filter which upon receiving a referencesignal generates a pseudo output for an unknown system; first means forgenerating a mixed signal from interference signals and an output signalof the unknown system; a first subtracter for subtracting the pseudooutput from said mixed signal; an information extraction circuit thatreceives the output signal of the adaptive filter to extract theinformation on the magnitude of coefficients for the adaptive filter andgenerate an output (a); an arithmetic circuit to receive the output (a)for calculating and providing a signal (b) which decreases as the output(a) increases or increases as the output (a) decreases; second means forcorrecting the coefficients of the adaptive filter utilizing the outputsfrom the first subtracter, said arithmetic circuit and the referencesignal; and said information extraction circuit comprising an absolutevalue circuit for developing an absolute value of the output of saidadaptive filter.
 16. Electronic filter apparatus as set forth in claim5, wherein said arithmetic circuit comprises a first average circuit foraveraging an input signal with a first parameter, a second averagecircuit for averaging the input signal with a second parameter thatdiffers from the first parameter in said first average circuit, and adivider for developing a ratio of an output of said first averagecircuit and an output of said second average circuit.
 17. Electronicfilter apparatus as in claim 15 wherein:said arithmetic circuitcomprises a first average circuit for averaging an input signal with afirst parameter, a second average circuit for averaging the input signalwith a second parameter that differs from the first parameter in saidfirst average circuit, and a divider for developing a ratio of an outputof said first average circuit and an output of second average circuit;and said divider comprises an inverter for outputting an inverted signalof the output from said second average circuit and a first multiplierfor multiplying the inverted signal with the output from said firstaverage circuit.
 18. A method of controlling coefficients of an adaptivefilter, said method comprising the steps of:obtaining a mixed signal bycombining an interference signal with an output signal from an unknownsystem; obtaining an output signal generated by said adaptive filter,and subtracting said output signal generated by said adaptive filterfrom said mixed signal to obtain a difference signal; obtaining a squarevalue of the output signal generated by the adaptive filter, andutilizing said square value of the output signal generated by theadaptive filter as obtained information relating to magnitude of theoutput signal of said adaptive filter; and adaptively varyingcorrections applied to the coefficients of said adaptive filteraccording to said obtained information.
 19. A method of controllingcoefficients of an adaptive filter, said method comprising the stepsof:obtaining a mixed signal by combining an interference signal with anoutput signal from an unknown system; obtaining an output signalgenerated by said adaptive filter, and subtracting said output signalgenerated by said adaptive filter from said mixed signal to obtain adifference signal; obtaining an absolute value of the output signalgenerated by the adaptive filter, and utilizing an absolute value of theoutput signal generated by the adaptive filter as obtained informationrelating to magnitude of the output signal of said adaptive filter; andadaptively varying corrections applied to the coefficients of saidadaptive filter according to said obtained information.